Multiple imputation in three or more stages

Missing values present challenges in the analysis of data across many areas of research. Handling incomplete data incorrectly can lead to bias, over-confident intervals, and inaccurate inferences. One principled method of handling incomplete data is multiple imputation. This article considers incomplete data in which values are missing for three or more qualitatively different reasons and applies a modified multiple imputation framework in the analysis of that data. Included are a proof of the methodology used for three-stage multiple imputation with its limiting distribution, an extension to more than three types of missing values, an extension to the ignorability assumption with proof, and simulations demonstrating that the estimator is unbiased and efficient under the ignorability assumption.